Case 10: Hotel Tourism
© Jostein Lillestøl NHH, Bergen
1
Hotel Tourism - Solution :
The part of the questionnaire made available is just on what is important when choosing vacation spot, and contains nothing specific to the hotels. Without more information we are therefore unable to answer the last question. We may be able to throw some light on the following:
What are the factors underlying the choice of vacation spot?
How can satisfaction be explained?
What separates the areas wrt. guest profile?
Which groups/segments exist within each area?
To get an understanding on the underlying decisive factors for choice of vacation spot, we may start by performing a factor analysis on the correlation matrix of the coded 19 responses to the given question from the questionnaire. These responses are ordinal on a 9-point scale, and not measured on a continuous (interval) scale required by the theory. In practice people are seldom worried about this. The uncovering of differences between the three locations may be based on the factor analysis or alternatively a discriminant analysis.
A so-called Scree plot of eigenvalues shows that 3 of them are well above one, and two slightly above one. This means that we will consider five underlying factors, possible reduced to three if no reasonable interpretation of the last two may be given. In the case of factor analysis on the covariance (or equivalently on the standardized variables) an eigenvalue less than one means a factor less important than a single variable.
.
18 16 14 12 10 8 6 4 2 4
3
2
1
0
Factor Number
Eigenvalue
Scree Plot of Nature; ...; Clean nature
Below is the result from an extraction of five factors from the correlation matrix of the 19
variables, using principal component extraction and varimax rotation. For brevity we omit the
details of the unrotated solution. We see that the 5 factors explain 52.9% of the (co)variation in
the 19 variables, which is more evenly distributed among the 5 factors in the rotated solution
than the unrotated one.
Case 10: Hotel Tourism
© Jostein Lillestøl NHH, Bergen
2 Factor Analysis: Nature; Bathing; Hiking; Entertainmen; Peace; Culture; Nice We
Principal Component Factor Analysis of the Correlation Matrix
Unrotated Factor Loadings and Communalities
570 cases used 199 cases contain missing values
…… omitted for brevity
Variance 3.7742 2.2995 1.6589 1.1764 1.1441 10.0531
% Var 0.199 0.121 0.087 0.062 0.060 0.529
Rotated Factor Loadings and Communalities Varimax Rotation
Variable Factor1 Factor2 Factor3 Factor4 Factor5 Communality Nature 0.293 -0.591 -0.058 -0.141 0.049 0.461 Bathing 0.001 0.088 -0.130 0.747 -0.029 0.583 Hiking 0.089 -0.320 -0.036 0.502 0.513 0.627 Entertainment 0.072 0.516 0.300 0.275 -0.269 0.509 Peace -0.175 -0.736 0.113 -0.065 -0.204 0.631 Culture 0.227 -0.232 0.570 -0.303 0.175 0.552 Nice Weather 0.254 -0.154 0.024 0.136 -0.690 0.584 New Exper 0.812 -0.015 0.031 -0.024 -0.234 0.716 Children friendly -0.178 0.183 0.072 0.667 -0.120 0.530 Good Food 0.200 -0.063 0.124 0.055 -0.673 0.515 Excursions 0.548 -0.169 0.260 -0.046 -0.159 0.424 Cheap 0.168 -0.275 0.369 -0.007 -0.381 0.386 Uncommon 0.739 0.018 0.188 -0.018 -0.169 0.610 Community 0.217 0.054 0.317 0.405 -0.203 0.356 Know area 0.497 -0.437 0.133 0.108 0.070 0.472 Get in shape 0.074 -0.166 0.448 0.481 0.134 0.483 Shopping -0.016 0.110 0.692 0.094 -0.328 0.608 Meet people 0.266 -0.020 0.634 0.058 -0.081 0.483 Clean nature 0.171 -0.650 0.162 0.060 -0.198 0.520
Variance 2.2520 2.1440 1.9363 1.8951 1.8257 10.0531
% Var 0.119 0.113 0.102 0.100 0.096 0.529 Factor Score Coefficients
Variable Factor1 Factor2 Factor3 Factor4 Factor5 Nature 0.107 -0.258 -0.103 -0.027 0.037 Bathing 0.044 -0.013 -0.164 0.419 -0.026 Hiking 0.100 -0.165 -0.024 0.310 0.339 Entertainment 0.024 0.264 0.145 0.085 -0.089 Peace -0.269 -0.412 0.046 -0.002 -0.182 Culture 0.018 -0.030 0.391 -0.203 0.229 Nice Weather 0.021 -0.086 -0.167 0.078 -0.421 New Exper 0.447 0.103 -0.170 -0.007 -0.025 Children friendly -0.105 0.022 0.006 0.345 -0.078 Good Food -0.016 -0.035 -0.072 0.017 -0.398 Excursions 0.232 0.001 0.042 -0.035 0.013 Cheap -0.069 -0.120 0.144 -0.024 -0.181 Uncommon 0.388 0.121 -0.038 -0.022 0.034 Community 0.053 0.039 0.103 0.189 -0.042 Know area 0.224 -0.153 -0.026 0.084 0.125 Get in shape -0.038 -0.080 0.256 0.235 0.171 Shopping -0.175 0.067 0.417 -0.029 -0.100 Meet people 0.025 0.053 0.361 -0.028 0.091 Clean nature -0.053 -0.321 0.006 0.061 -0.11
Case 10: Hotel Tourism
© Jostein Lillestøl NHH, Bergen
3 The each factor of the rotated solution we may look at the size (in absolute value) of its factor loadings, in order see what characterizes the variables that load on this factor. From this we are tempted to give the five factors the following interpretation:
Factor 1: Adventures (Uncommon, New experience)
Factor 2: Environment (Peace, Cleanliness, Nature) vs Entertainment Factor 3: Town activity (Shopping, Meet people, Culture)
Factor 4: Physical activity (Bathing, Hiking, Get in shape, Children friendly) Factor 5: Passive enjoyment (Good Food, Nice weather) vs Active (Hiking)
Factor 2 and 5 are so-called bipolar factor with both large positive and negative coefficients that separates two categories of people measured along a dimension.
While the factor loadings express how each variable is determined linearly by the five unobserved underlying (latent) factors, the factor scores express how each (unobserved) factor is determined as a linear combination of the 19 observed variables. This may be computed for all respondents having answered all 19 items. The result may be presented graphically in several different manners. One is by a collection of box-plots, displaying the median, quartile range, the enlarged range and the outlying scores. We see that Region 1 (Valleyland) has the highest median score on Factor 3 (Town activity), Region 2 (Fjordland) highest on Factor 5 (Passive enjoyment vs, hiking) and Region 3 (Coastland) highest on Factor 1 and 4 (Adventures and Physical activity).
For Factor 2 (Environment vs Entertainment) the medians in the three regions are about equal.
This may make sense to those who know the actual regions, which are Voss, Stryn and
Vesterålen respectively. From the plot we may also see the regions with lowest median score and the ones with small and large variation in scores and possibly give sensible interpretations.
Region
Factorscore 5 Factorscore 4
Factorscore 3 Factorscore 2
Factorscore 1
3 2 1 3 2 1 3 2 1 3 2 1 3 2 1 5 4 3 2 1 0 -1 -2 -3 -4
Score
Boxplot of Factorscores for 5 factors for each of 3 regions
Case 10: Hotel Tourism
© Jostein Lillestøl NHH, Bergen
4
We may alternatively perform a discriminant analysis, where the observed 19 variables are used as predictors of Region. Here is the output, where the coefficients for three linear predictor formulas are listed at the end. For a respondent, take the 19 coded answers, weigh them by the coefficients and sum. The respondent is then “predicted” to belong to the region with highest score. The importance of the various variables in the prediction may be judged from the coefficients. For instance Culture is given more weight in being classified to Region 1 than the other regions. The output also contains information on how successful the procedure was to “predict” the actual observation, as an indication on a lower limit to success in predicting new observations. An alternative mode of discriminant analysis exists, more directed towards response profiles.
Discriminant Analysis: Region versus Nature; Bathing; ...
Linear Method for Response: Region
Predictors: Nature; Bathing; Hiking; Entertainment; Peace; Culture;
Nice Weather; New Exper; Children friendly; Good Food; Excursions;
Cheap; Uncommon; Community; Know area; Get in shape; Shopping;
Meet people; Clean nature
Group 1 2 3 Count 346 166 58
570 cases used, 199 cases contain missing values Summary of classification
True Group Put into Group 1 2 3 1 208 52 14 2 82 69 9 3 56 45 35 Total N 346 166 58 N correct 208 69 35 Proportion 0.601 0.416 0.603
N = 570 N Correct = 312 Proportion Correct = 0.547 Squared Distance Between Groups
1 2 3 1 0.00000 0.71126 1.40987 2 0.71126 0.00000 1.03271 3 1.40987 1.03271 0.00000
Linear Discriminant Function for Groups
1 2 3 Constant -43.071 -41.179 -47.197 Nature 4.843 4.944 5.275 Bathing 0.904 0.965 0.975 Hiking 0.282 0.467 0.378 Entertainment 1.158 1.121 0.992 Peace 0.669 0.648 0.456 Culture 0.409 0.296 0.162 Nice Weather 0.741 0.626 0.884 New Exper 1.947 1.789 1.872 Children friendly 0.694 0.899 1.163 Good Food 0.533 0.652 0.713 Excursions 0.375 0.453 0.383 Cheap 0.584 0.520 0.448 Uncommon -0.358 -0.427 -0.171 Community 0.104 0.064 0.056 Know area 0.815 0.745 0.933 Get in shape -0.059 -0.133 -0.049 Shopping 0.004 -0.117 -0.099 Meet people 0.098 0.146 0.141 Clean nature 2.105 1.962 2.133
